Development of special optical fibers for evanescent-wave chemical sensing

The paper summarizes results achieved in the Institute of Radio Engineering and Electronics in the field of investigation and fabrication of novel fiber-optic structures for evanescent-wave chemical sensing. Several approaches for increasing the evanescent-wave sensitivity of multimode silica optical fibers to gaseous and liquid chemicals are shown. These approaches make use of the decrease of the core diameter in sectorial and capillary sectorial fibers, modification of trajectories of optical rays in the cores of inverted-graded-index fibers, tailoring of the refractive index of porous layers applied on silica cores, an output mode filter preventing the detection of rays propagating at low axial angles or fibers bent in single or multiple turns. Presented at the 1st Czech-Chinese Workshop “Advanced Materials for Optoelectronics”, Prague, Czech Republic, June 13–17, 1998. This work was supported by the Grant Agency of the Czech Republic (projects No. 102/96/0939 and No. 102/98/1358) and by joint project No. 4104 of AS CR and CNRS, France.     

Regularity of ultrafilters

If there arek ⁺⁺ eventually functions fromk ⁺ intok or if there arek ⁺⁺ eventually different functions fromk ⁺ then uniform ultrafilters onk ⁺ are (k, k ⁺)-regular. The research of the first author was supported in part by NSF grant. The second author is a Miller’s Fellow at the University of California in Berkeley.     

A theory of non-radiative transfer of excitation energy in solids

A theory of non-radiative transfer of excitation energy in solids is elaborated for the case of strong interaction of an atom of the sensitizer and an atom of the activator with the oscillations of the whole crystal lattice.     

Ein Detektor Langsamer Neutronen

Zusammenfassung Der Scintilationsdetektor für Thermo-und Resonanzneutronen, der in dieser Arbeit beschrieben wird, wurde aus einem geschmolzenen Gemisch von ZnS(Ag) und ₂₃ hergestellt. Bei optimalem Verhältnis beider Komponenten und optimaler Dicke des Detektors kann für Thermoneutronen eine verhältnismässig grosse Wirksamkeit erzielt werden (bis 25%). Der Detektor kann auch bei starkem Hintergrund von -Strahlung benützt werden, da die Wirksamkeit der -Strahlregistrierung durch passende Einstellung des Diskriminators unter 10^–7% herabgesetzt werden kann, bei einer Wirksamkeit für Thermoneutronen von ungefähr 6%.     

Toeplitz Operators and Group Representations

Toeplitz operators on the Bergman space of the unit disc can be written as integrals of the symbol against an invariant operator field of rank-one projections. We consider a generalization of the Toeplitz calculus obtained upon taking more general invariant operator fields, and also allowing more general domains than the disc; such calculi were recently introduced and studied by Arazy and Upmeier, but also turn up as localization operators in time-frequency analysis (witnessed by recent articles by Wong and others) and in representation theory and mathematical physics. In particular, we establish basic properties like boundedness or Schatten class membership of the resulting operators. A further generalization to the setting when there is no group action present is also discussed, and the various settings in which similar operator calculi appear are briefly surveyed.     

Littlewood-Paley inequalities in uniformly convex and uniformly smooth Banach spaces

It is proved that the inequality δX(ε)?cεp, p?2, where δX is the modulus of convexity of X, is sufficient and necessary for the inequality

     

CASPT2 and CCSD(T) calculations of dipole moments and polarizabilities of acetone in excited states

The acetone molecule is investigated in its ground state and valence ^1,3n-π*, ^1,3π-π*, and ^1,3σ-π* excited states and Rydberg ^1,3n-3s, ^1,3π-3?, ^1,3n-3p_y and ^1,3π-3p_y states using the CASSCF, CASPT2, and CCSD(T) methods. Equilibrium geometries of excited states are obtained and their changes with respect to the ground state are discussed. For most excited states the C_2v symmetry of the ground state is lowered to the C_s symmetry. A series of valence vertical and adiabatic excitation energies is presented along with excitation energies for Rydberg states. The main body of the paper contains Finite-Field Perturbation Theory (FFPT) calculations of electric properties of the vertically as well as geometry relaxed excited states. Dipole moments of valence excited states decrease significantly upon excitation, being about one half of the ground state dipole moment. Polarizabilities usually change upon excitation much less (increase by about 30%) but hyperpolarizabilities are enhanced up to one or two orders of magnitude. The orientation of the dipole moment is reversed in some vertically excited Rydberg states. Properties of the ground and excited states are discussed considering alterations of the electronic structure and shifts in the geometry.     

Some open categorical problems inTop

In this paper, a pendant to a recent survey paper, the authors discuss several open problems in categorical topology. The emphasis is on topology-oriented problems rather than on more general category-oriented ones. In fact, most problems deal with full subconstructs or superconstructs of the constructTop of topological spaces and continuous maps.     

Sums and Limits of Generalized Direct Families of Algebras

In this paper we introduce a generalization of direct families of algebras and we study their limits and sums. In the case of generalized direct families of algebras carried by idempotent algebras we investigate some subdirect decompositions of their sums. The results that we obtain generalize various results given by J.L. Chrislock and T. Tamura [2], M. iri and S. Bogdanovi [3-7], H. Mitsch [13], M. Petrich [14-16], B.M. Schein [23-24] and others.Supported by Grant 04M03B of RFNS through Math. Inst. SANU     

Recurrence relations for orthogonal rational functions

It is well known that members of families of polynomials, that are orthogonal with respect to an inner product determined by a nonnegative measure on the real axis, satisfy a three-term recursion relation. Analogous recursion formulas are available for orthogonal Laurent polynomials with a pole at the origin. This paper investigates recursion relations for orthogonal rational functions with arbitrary prescribed real or complex conjugate poles. The number of terms in the recursion relation is shown to be related to the structure of the orthogonal rational functions.